Engineering Rock Mechanics

170 Anisotropy and inhomogeneity

process repeated for different size groups of data. The ’step’ in these
plots indicates the approximate location of the boundary, and possibly
a structural domain boundary. The results of groups of 9,10,11, 12, 13,
and 14 values are shown below.

* 11 values --X. 12 values

-0- 13 values --+-- 14 values

6.50 7.50 8.50 9.50 10.50 11.50 12.50

location along borehole core, rn

It is evident from this graph that there is a definite change in the mean

spacing value at about 11 m: before 11 m, the mean value is about 0.38 m;

after 11 m, the mean value reduces to about 0.26 m. As a result, we can

say that there is some change in the underlying spacing data at about the

11 m position.

One of the features of presenting data smoothed through the use of

moving averages is that there may be a shifting in the peaks and troughs

of the smoothed curves. As Davis (1973) has noted, “A moving average

will ’lead’ an upward run in the data; that is, the smoothed curve will

rise at a greater rate than the data themselves. Likewise, the smoothed

curve will ’trail’ a downward run.” Thus, in the curves above we would

anticipate that the stratigraphic boundary will be at a position slightly

less than 11 m. Davis goes on to explain that when such smoothing

techniques are applied to data such as seismic records, the process is

called ’filtering’ and the smoothed logs are often easier to correlate with

geological boundaries. The major, or long-term, features of the record

are emphasized at the expense of short-term variations, known as ’loss

of high frequencies’. The smoothing is called a ’low-pass filter’.

For the current question, the identification of a stratigraphic boundary

between two units of limestone, the smoothing process as a low-pass

filter is precisely what is required, and enables the clearer identification

of the boundary, as illustrated. Note that in this question, the spatial

location of the fracture events has been taken into account because we

have explicitly used the position of the fractures. In classical statistical

analysis, such location is not generally taken into account. Because

the spatial information is critical, e.g. for deciding on the location of

Davis J. C. (1973) Statistics and Data Analysis in Geology. Wiley, New York, 55Opp.